I am wondering if the biometric information collected by Apple's Health app stays local on my iPhone, or if it's being sent to Apple?
Unless you choose to backup your data to iCloud, none of your data will be sent to Apple. Even if you do choose to backup your data to iCloud, that data is encrypted - meaning only you can access it.
- https://www.apple.com/legal/privacy/en-ww/ (Read about policies and related links)
- http://privacy.apple.com/ (Sign in and get your data)
To quote Apple directly:
In a nutshell, only you (or anyone who knows your passcode or has a fingerprint set on your iPhone) have control of your health data.
Someone should contact Apple’s privacy officer to get an answer. Here, perhaps.
PS: The false claim that “data is encrypted” - means “only you can access it” is dangerous misinformation. See, eg Secrets and Lies: Digital Security in a Networked World By Bruce Schneier , Chapter 13 on Key Escrow, AKA GAK, etc.
Specifically, it is well documented by Apple that it’s at least sometimes the case that even though on Apple devices, a user’s data is encrypted, Apple has access to it due to Key Escrow, that is, it is NOT the case that “only you can access it” see link in my comment on the other answer.